Related papers: Improved generalization with deep neural operators…

In this paper, we consider the design of model predictive control (MPC) algorithms based on deep operator neural networks (DeepONets). These neural networks are capable of accurately approximating real and complex valued solutions of…

We present a data-driven control framework for partial differential equations (PDEs). Our approach integrates Time-Integrated Deep Operator Networks (TI-DeepONets) as differentiable PDE surrogate models within the Differentiable Predictive…

Optical Diffraction Neural Networks (DNNs), a subset of Optical Neural Networks (ONNs), show promise in mirroring the prowess of electronic networks. This study introduces the Hybrid Diffraction Neural Network (HDNN), a novel architecture…

To derive the hidden dynamics from observed data is one of the fundamental but also challenging problems in many different fields. In this study, we propose a new type of interpretable network called the ordinary differential equation…

In recent times machine learning methods have made significant advances in becoming a useful tool for analyzing physical systems. A particularly active area in this theme has been "physics-informed machine learning" which focuses on using…

Solving parametric partial differential equations (PDEs) and associated PDE-based, inverse problems is a central task in engineering and physics, yet existing neural operator methods struggle with high-dimensional, discontinuous inputs and…

The operator learning has received significant attention in recent years, with the aim of learning a mapping between function spaces. Prior works have proposed deep neural networks (DNNs) for learning such a mapping, enabling the learning…

Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in practical applications like the irregular mesh, multiple input…

Poroelasticity -- coupled fluid flow and elastic deformation in porous media -- often involves spatially variable permeability, especially in subsurface systems. In such cases, simulations with random permeability fields are widely used for…

A large class of hyperbolic and advection-dominated PDEs can have solutions with discontinuities. This paper investigates, both theoretically and empirically, the operator learning of PDEs with discontinuous solutions. We rigorously prove,…

Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical operators. In the present work, we introduce Mesh-Informed…

Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the…

Developing neural operators that accurately predict the behavior of systems governed by partial differential equations (PDEs) across unseen parameter regimes is crucial for robust generalization in scientific and engineering applications.…

Accurately learning solution operators for time-dependent partial differential equations (PDEs) from sparse and irregular data remains a challenging task. Recurrent DeepONet extensions inherit the discrete-time limitations of…

This work explores the application of deep operator learning principles to a problem in statistical physics. Specifically, we consider the linear kinetic equation, consisting of a differential advection operator and an integral collision…

Continuous deep learning models, referred to as Neural Ordinary Differential Equations (Neural ODEs), have received considerable attention over the last several years. Despite their burgeoning impact, there is a lack of formal analysis…

Deep neural operators can learn operators mapping between infinite-dimensional function spaces via deep neural networks and have become an emerging paradigm of scientific machine learning. However, training neural operators usually requires…

As overparameterized models become increasingly prevalent, training loss alone offers limited insight into generalization performance. While smoothness has been linked to improved generalization across various settings, directly enforcing…

We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries. Classical geometric learning methods typically represent domains as meshes, graphs, or point clouds. Our…

Traditional numerical schemes for simulating fluid flow and transport in porous media can be computationally expensive. Advances in machine learning for scientific computing have the potential to help speed up the simulation time in many…